Scale drawings | Year 11 | Ascent Library

01 / LEARN

The idea, step by step

Understand the idea

A scale of $1 : n$ means one drawing unit represents $n$ of the same real unit. Convert units before comparing. At 1:100, 1 cm on paper represents 100 cm, which is 1 m, in reality.

Lengths change by the linear factor, areas by its square, and volumes by its cube. A solid doubled in every dimension has four times the surface area and eight times the volume.

Choose and apply a method

Translate the scale into a useful unit statement. At 1:200, 1 cm represents 2 m. Multiply a drawing length to obtain a real length, or divide a real length to obtain the drawing length.

Use stated measurements rather than measuring an image on a screen. Resizing changes a printed scale. If a drawing must be physically to scale, specify paper size and verify a reference length after printing.

real length = n \times drawing length (same units)

A common trap

Applying the linear factor directly to area.

Instead: Convert both lengths first, or use the square of the linear factor.

02 / WORKED EXAMPLES

See the thinking

Example 1

Read a floor plan

A room is 4.5 cm by 3 cm on a 1:200 plan. Find its actual dimensions and area.

1 cm represents 2 m.
Dimensions are $4.5 \times 2 = 9$ m and $3 \times 2 = 6$ m.
Floor area $= 9 \times 6 = 54$ m $2$ .

9 m by 6 m; 54 m

2

Example 2

Draw a length

A 12 m path is shown at 1:150. Find its drawing length.

12 m is 1200 cm.
Drawing length $= 1200 / 150 = 8$ cm.

8 cm.

Check your understanding

At 1:50, what real length does 6 cm represent?

Show answer

3 m.

$6 \times 50 = 300$ cm $= 3$ m.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

At 1:100, a plan wall is 7.2 cm long. Find its real length.
2 marks
A 9 m fence is drawn at 1:300. Find its drawing length.
2 marks
A 1:250 plan shows a rectangle 4 cm by 2 cm. Find real area.
2 marks
Similar solids have corresponding lengths in ratio 2:3. Find their volume ratio.
2 marks
A model has area 24 cm $2$ . An enlargement triples every length. Find new area.
2 marks
A 1:10,000 map is reduced to half its original linear size. Find the new scale.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

At 1:100, a plan wall is 7.2 cm long. Find its real length.
2 marks
$7.2 \times 100 = 720$ cm $= 7.2$ m.
7.2 m.
A 9 m fence is drawn at 1:300. Find its drawing length.
2 marks
$900 / 300 = 3$ cm.
3 cm.
A 1:250 plan shows a rectangle 4 cm by 2 cm. Find real area.
2 marks
1 cm represents 2.5 m.
The real rectangle is 10 m by 5 m, so its area is 50 m $2$ .
50 m $2$ .
Similar solids have corresponding lengths in ratio 2:3. Find their volume ratio.
2 marks
Cube the linear factors: $2^{3} : 3^{3} = 8 : 27$ .
8:27.
A model has area 24 cm $2$ . An enlargement triples every length. Find new area.
2 marks
The area factor is $3^{2} = 9$ ; $24 \times 9 = 216$ .
216 cm $2$ .
A 1:10,000 map is reduced to half its original linear size. Find the new scale.
2 marks
The same real length now uses half the paper length, so the denominator doubles.
1:20,000.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

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